For use in a strictly stereo music re-production system (or HiFi - to the old guard), an integrated amplifier includes all the audio inputs required for such a system including digital inputs and a phono stage for use with a turntable. The vast majority also include AM/FM tuners with some also offering DAB radio.
The key difference between the Integrated Amplifier and the Pre-Amplifier is the amplifiers which are included in the Integrated Amplifier. You will usually find two channels of amplification built-in, offering enough power to drive two fairly large speakers.
Popular brands include Cambridge Audio, Arcam, Denon, Meridian, Pioneer and Onkyo